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Although the Web lets users freely browse and publish information, most Web information is unauthorized in contrast to conventional mass media. Therefore, it is not always credible or correct. We propose a model to solve these problems by enabling the credibility of text-image pairs on the Web to be analyzed. We propose a bipartite graph model, in which one set of nodes corresponds to a set of text data, and the other corresponds to a set of images. That is, each text-image pair is represented by an edge. We introduce the notion of "supportive relationships" among edges in our bipartite graph model. Intuitively, our hypothesis is that the more "supportive" text-image pairs a target text-image pair has, the more credible it is. Although such a bipartite graph model is by itself not necessarily new, one of its most notable features is that we take into consideration the similarity (or dissimilarity) among nodes in each node set to compute supportive relationships. As our model is generic, it can be applied to a variety of types of Web information represented by text-image pairs. We especially focus on the analysis of text-image pairs on the Web in this paper and describe a practical implementation of our model for analyzing credibility, ImageAlert.